On Lamperti transformation and AR$(1)$ type characterisations of discrete random fields
Authors:
Marko Voutilainen, Lauri Viitasaari and Pauliina Ilmonen
Journal:
Theor. Probability and Math. Statist. 111 (2024), 181-197
MSC (2020):
Primary 60G60, 60G10, 60G18
DOI:
https://doi.org/10.1090/tpms/1222
Published electronically:
October 30, 2024
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Additional Information
Abstract: In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections between stationary fields, stationary increment fields and, through Lamperti transformation, self-similar fields. Our contribution is a natural generalisation of recently proved results covering the case of stationary processes.
References
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References
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- M. Clausel, Gaussian fields satisfying simultaneous operator scaling relations, Recent Developments in Fractals and Related Fields, Springer, 2010, pp. 327–341. MR 2743003
- P. Embrechts, Selfsimilar processes, Princeton Series in Applied Mathematics, Princeton University Press, 2002. MR 1920153
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- M. Voutilainen, Modeling and estimation of multivariate discrete and continuous time stationary processes, Front. Appl. Math. Stat. 6 (2020).
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- M. Voutilainen, L. Viitasaari, P. Ilmonen, S. Torres, and C. Tudor, Vector-valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimation, Scand. J. Stat. 49 (2022), no. 3, 992–1022. MR 4471277
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Additional Information
Marko Voutilainen
Affiliation:
Turku School of Economics, Department of Accounting and Finance, FI-20014 University of Turku, Finland
Email:
mtvout@utu.fi
Lauri Viitasaari
Affiliation:
Uppsala University, Department of Mathematics, Box 480, 751 06 Uppsala, Sweden
Address at time of publication:
Aalto University, Department of Information and Service Management, P.O. Box 21210, 00076 Aalto, Finland
Email:
lauri.viitasaari@aalto.fi
Pauliina Ilmonen
Affiliation:
Aalto University, Department of Mathematics and Systems Analysis, P.O. Box 11100, FI-00076 Aalto, Finland
Email:
pauliina.ilmonen@aalto.fi
Keywords:
Random fields,
stationary fields,
self-similar fields,
Lamperti transformation,
fractional Ornstein–Uhlenbeck fields
Received by editor(s):
April 21, 2023
Accepted for publication:
September 7, 2023
Published electronically:
October 30, 2024
Additional Notes:
Academy of Finland, decision number 346308
Article copyright:
© Copyright 2024
Taras Shevchenko National University of Kyiv
